Question

Find the length of dm in the given fig.​

Answer 1

`DM=12`

Explanation:

(Let the point where the altitude from
`D` intersects
`AB` be called as point
`E`.) First, let's find the area of parallelogram
`ABCD`. The area of a parallelogram is simply
`b*h=bh`, where
`b` is the parallelogram's base and
`h` is the parallelogram's height. If we let
`AB` and
`DE` be the base and height respectively, since we are already given their lengths, we know that the area of parallelogram
`ABCD` will be
`AB*DE=15*8=120`.

Now, how does this information matter, you might ask? Well, we can take either
`AB` or
`CB` to be the base and either
`DE` or
`DM` to be the height. In this case, let's take the latter two options, as we are looking to find the length of
`DM`.

Therefore, we know that the area of parallelogram
`ABCD` can also be found by calculating
`CB*DM`. Since we know the values of the area and
`CB`, we can write the following equation to solve for
`DM`:

`Area = CB*DM`

`120=10*DM` (Substitute
`Area=120` and
`CB=10` into the equation)

`(120)/(10)=(10*DM)/(10)` (Divide both sides of the equation by
`10` to get rid of
`DM`'s coefficient)

`12=DM` (Simplify)

`DM=12` (Symmetric Property of Equality)

Hope this helps!